Adding a genus ID after the more specific species ID won’t really attract any more attention to an observation, except for the very small number of people who might sort observations by “last updated”.
The only way it would hinder an observation from more quickly achieving research grade is if you had accidentally added a disagreeing genus ID (orange button) instead of without disagreeing (green button). I pretty rarely use that green button myself. I wonder if whoever said that is just mistaken about how IDs work. I’m happy to take a look at the observation if you want to send the link to me in a personal message.
For more discussion on the disagreeing ID pop-up language, see https://forum.inaturalist.org/t/change-wording-used-by-the-system-when-downgrading-an-observation-to-an-higher-level-taxa/3862/